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jobu
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Homework Statement
This problem isn't actually assigned homework for me, but I wanted to see if I get the concept. Any feedback and corrections to my answer would be appreciated!
A cable is stretched between two anchors, and a small mass is attached to the cable, through the center of the mass, at the cable midpoint. The cable is made of a linear, elastic material. Gravity is not a factor in this model.
1) the mass is pulled down and released, so that a transverse oscillation in created in the cable. Will increasing the tension in the cable in crease the oscillation frequency of the mass, Why or why not?
2) the mass is pulled towards one anchor and released, creating an oscillation along the axis of the cable. What effect will increasing tension have on the oscillation frequency?
Homework Equations
cable acts like a linear spring - Tension T = k*x
k is the spring constant of the cable
x is the difference in the length of the stretched cable versus the unstretched cable (no tension).
The Attempt at a Solution
for the first part, I think that the increase in tension WILL increase the frequency of the mass oscillation. Whenever the mass moves out of line with the anchored cable endpoints, a vertical component of the tension accelerates the mass back towards that axis. Increasing tension in the cable will increase that vertical force component, and the acceleration on the mass. The mass will change velocity more quickly, and so complete the oscillation cycle more quickly ... increasing the frequency.
For the axial oscillation, the increase in tension will have no effect on the mass oscillation. Since tension acts towards both anchors with equal magnitude, any change in cable tension will also increase the forces acting on the mass towards each anchor equally. The changes in force cancel each other out, and the mass oscillates at the original frequency.
Is that reasoning correct?
Thanks!